https://doi.org/10.1016/j.jrmge.2025.04.018

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鈣質砂的應力–應變特性受顆粒破碎（B）與初始相對密度（Dri）顯著影響，但現(xiàn)有本構模型極少同時考慮二者的耦合作用。為填補這一空白，本文針對不同Dri和應力路徑的鈣質砂開展系列三軸試驗，系統(tǒng)研究顆粒破碎與臨界狀態(tài)行為。

主要發(fā)現(xiàn)如下：（1）當應力比（η）恒定時，B隨平均有效應力（p'）呈雙曲線關系；給定p'下，B隨η線性增大；（2）臨界狀態(tài)線（CSL）隨Dri增大而下移，而臨界狀態(tài)摩擦角（φcs）隨B增大而減小?；谏鲜鼋Y果，提出統(tǒng)一的顆粒破碎演化模型，用以量化不同加載條件下鈣質砂的破碎程度。將該模型與正常固結線（NCL）及CSL方程耦合，成功再現(xiàn)隨B增大、NCL與CSL斜率增大的現(xiàn)象，并定量評估B對φcs的影響。最后，在臨界狀態(tài)土力學與亞塑性理論框架內，建立了同時引入B與Dri的亞塑性模型；該模型在不同初始相對密度、應力路徑及排水條件下的模擬結果與試驗數(shù)據高度吻合，驗證了其可靠性。

Fig. 1. Physical properties of calcareous sand: (a) SEM image; and (b) Grain size distribution (GSD) curve of calcareous sand.

Fig. 2. Test schematic and apparatus: (a) Test schematic; and (b) GDS triaxial automated system.

Fig. 3. Effect of initial densities on the triaxial test results of calcareous sand: (a-b) CTC test, p_c=200 kPa; (c-d) TC test, p_c=200 kPa; (e-f) RTC test, p_c=200 kPa; (g-h) CU test, p_c=200 kPa; (i-j) CTC test, p_c=800 kPa; (k-l) TC test, p_c=800 kPa; (m-n) RTC test, p_c=800 kPa; and (o-p) CU test, p_c=800 kPa

Fig. 4. Variation in GSD curves of calcareous sand and relationship between B with p′ and η: (a-b) Effect of D_ri; (c-d) Effect of p_c; and (e-f) Effect of loading path.

Fig. 5. Relationship between B with p' and η: (a) B- log₁₀ p' relation; and (b) Determination of ω₀ and k_ω (Solid colourful lines represent simulation results by Eq. (8))

Fig. 6. Stress ratio of calcareous sand sheared to maximum axial strain: (a) CTC test; (b) TC test; (c) RTC test; and (d) CU test.

Fig. 7. Comparison of B-p' relations with different test results: (a) Dogs Bay sand; (b) Angular granite (PL: Proportional loading); and (c) Decomposed granite.

Fig. 8. Predicted and measured NCLs of calcareous sand with various initial densities. (a) Predicted versus experimental test results; (b) Influence of k_Dr (Eq. (36)); and (c) Influence of k_B (Eq. (36)).

Fig. 9. Predicted and measured CSLs of calcareous sand with various initial densities: (a) D_ri=0.1; (b) D_ri =0.3; (c) D_ri =0.6; and (d) D_ri =0.9.

Fig. 10. Schematic of the effect of particle breakage on the location of CSL in e-log₁₀p' plane

Fig. 11. Influence of parameter χ and β on predicted results: (a) Effect of χ (Eq. (44)); and (b) Effect of β (Eq. (44)).

Fig. 12. Relationship between critical friction angle φ_cs with particle breakage B of calcareous sand: (a) Experimental data; and (b) Effect of χ_B on predicted M_cs (Eq. (48)).

Fig. 13. Influence of breakage evolution parameters on model prediction results in drained triaxial test: (a-b) Effect of ω₀; (c-d) Effect of k_ω; and (e-f) Effect of p_B.

Fig. 14. Influence of initial density effect parameters on model prediction results in drained triaxial test: (a-b) Effect of D_ri; (c-d) Effect of k_Dr; and (e-f) Effect of χ.

Fig. 15. Influence of breakage effect parameters on model prediction results in drained triaxial test: (a-b) Effect of k_B; (c-d) Effect of β; and (e-f) Effect of χB.

Fig. 16. Comparison between model predictions with CTC tests results of calcareous sand at different D_ri: (a-b) D_ri =0.1; (c-d) D_ri =0.3; (e-f) D_ri =0.6; and (g-h) D_ri =0.9.

Fig. 18. Comparison between model predictions with TC tests results of calcareous sand at different D_ri: (a-b) D_ri =0.1; (c-d) D_ri =0.3; (e-f) D_ri =0.6; and (g-h) D_ri =0.9.

Fig. 20. Comparison of the predicted and measured values of B

Fig. 21. Change in GSD of calcareous sand with D_ri=0.1:(a-b) CTC test; (c-d) TC test; (e-f) RTC test; and (g-h) CU test.

Fig. 22 Comparison between model predictions with drained triaxial tests results of Silica sand at different D_ri: (a-b) D_ri =0.30; (c-d) D_ri =0.60; and (e-f) D_ri=0.90.

現(xiàn)有本構模型未能充分考慮顆粒破碎（B）與初始相對密度（D_ri）對鈣質砂的耦合影響。為此，本文開展了系列三軸壓縮試驗，涵蓋不同D_ri、應力路徑與排水條件。基于試驗結果，提出了新的破碎演化模型，并修正了正常固結線（NCL）與臨界狀態(tài)線（CSL）方程，以同時納入B與D_ri的聯(lián)合作用。隨后，將這些公式嵌入亞塑性框架，建立了改進的亞塑性本構模型。主要結論如下：

（1）三軸試驗表明，B與D_ri對強度與變形具有顯著且相互依賴的影響。低圍壓下B較小，D_ri起主導作用；隨圍壓增大，B增加，D_ri的影響減弱。

（2）顆粒破碎主要受應力比η與平均有效應力p′控制。η恒定時，B隨p′增大而升高；p′恒定時，B與η成正比。提出的雙曲線破碎演化模型僅需3個易標定參數(shù)，即可描述不同應力路徑、D_ri與圍壓下的破碎行為。

（3）新NCL與CSL方程可準確反映隨B增大而陡化、隨D_ri增大而下移的規(guī)律；臨界狀態(tài)摩擦角φ_cs隨B線性降低。

（4）將破碎演化模型與修正NCL、CSL方程融入亞塑性框架，建立了可同時考慮顆粒破碎與初始密度的擴展亞塑性模型，可精確預測級配演化、強度與變形。

盡管模型預測性能良好，但驗證僅限于等向固結與單調加載。實際島礁與離岸工程常面臨各向異性應力與風浪循環(huán)荷載，后續(xù)研究將拓展模型至這些復雜工況，提升其工程適用性。

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